Question

Help!! Prove that: (tan u + cot u)/(tan u - cot u)= 1/sin^2u-cos^2u

Answer 1

change in sin and cos and simplify

Answer 2

How do you change in sin and cos?

Answer 3

\[\left( \frac{ \tan u+\cot u }{ \tan u-\cot u } \right)=\frac{ \left( \frac{ \sin u }{ \cos u }+\frac{ \cos u }{ \sin u } \right) }{ \left( \frac{ \sin u }{ \cos u }-\frac{ \cos u }{ \sin u } \right) }\]
\[=\frac{ \frac{ \sin ^2u+\cos ^2u }{ \sin u~\cos u } }{ \frac{ \sin ^2u-\cos ^2u }{ \sin u~\cos u } }\]
\[=\frac{ 1 }{ \sin u~\cos u }\times \frac{ \sin u~\cos u }{ \sin ^2u-\cos ^2u }=?\]

Answer 4

It would equal 1/sin u-cos u?

Answer 5

\[=\frac{ 1 }{ \sin ^2u-\cos ^2u }\]

Answer 6

Thanks again! You're awesome :)

Answer 7

yw